Respuesta :

The mentioned question can be solved with the help of Henderson-Hasselbalch equation. In biochemistry and chemistry, the Henderson-Hasselbalch equation can be used to find out the pH of a buffer solution comprising given concentrations of an acid and its conjugate base.

By using Henderson-Hasselbalch equation:

pH = pKa + log ([HCO³⁻] / [H₂CO₃])

pH = -log Ka + log ([HCO³⁻] / [H₂CO₃])

7.2 = -log (4.3 × 10⁻⁷) + log ([HCO³⁻] / [H₂CO₃])

log ([HCO³⁻] / [H₂CO₃]) = 0.83347

[HCO³⁻] / [H₂CO₃] = 10^0.83 = 6.8

Hence, the ratio of HCO³⁻ to H₂CO₃ in an exhausted runner would be 6.8 to 1.

BladeRunner212

6.815 : 1

Further explanation

The Problem:

The ratio of HCO₃⁻ to H₂CO₃ in an exhausted marathon runner whose blood pH is 7.2.

The Process:

  • The acid-dissociation constant values, Ka, for carbonic acid, H₂CO₃, is 4.3 x 10⁻⁷.  
  • HCO₃⁻ and H₂CO₃ are conjugate acid-base pairs
  • HCO₃⁻ and H₂CO₃ form an acidic buffer system.

To calculate the specific pH of a given buffer, we need using The Henderson-Hasselbalch equation for acidic buffers:

[tex]\boxed{ \ pH = pK_a + log\frac{[A^-]}{[HA]} \ }[/tex]

where,  

  • Ka represents the dissociation constant for the weak acid;
  • [A-] represent the concentration of the conjugate base (i.e. salt);  
  • [HA] is the concentration of the weak acid.

But keep in mind, in our problem the question is what is the ratio of HCO₃⁻ to H₂CO₃.

[tex]\boxed{ \ pH = pK_a + log\frac{[HCO_3^-]}{[H_2CO_3]} \ }[/tex]

[tex]\boxed{ \ 7.2 = -log(4.3 \times 10^{-7}) + log\frac{[HCO_3^-]}{[H_2CO_3]} \ }[/tex]

[tex]\boxed{ \ 7.2 = 7-log \ 4.3 + log\frac{[HCO_3^-]}{[H_2CO_3]} \ }[/tex]

[tex]\boxed{ \ log\frac{[HCO_3^-]}{[H_2CO_3]} = 7.2 - 7 + log \ 4.3\ }[/tex]

[tex]\boxed{ \ log\frac{[HCO_3^-]}{[H_2CO_3]} = 7.2 - 7 + 0.633 \ }[/tex]

[tex]\boxed{ \ log\frac{[HCO_3^-]}{[H_2CO_3]} = 0.833 \ }[/tex]

[tex]\boxed{ \ \frac{[HCO_3^-]}{[H_2CO_3]} = 10^{0.833} \ }[/tex]

[tex]\boxed{ \ \frac{[HCO_3^-]}{[H_2CO_3]} = 6.815 \ }[/tex]

Thus, the ratio of HCO₃⁻ to H₂CO₃ equal to 6.815 : 1.

_ _ _ _ _ _ _ _ _ _

Notes

  • The carbonate buffer system plays a role in regulating blood pH levels.
  • The phosphate buffer system, i.e., HPO₄²⁻ and H₂PO₄⁻ play a role in plasma and erythrocytes.

Learn more

  1. What is the pH of this buffer https://brainly.com/question/11437567
  2. Calculate the percent ionization (α) of formic acid solutions having the following concentrations (M). https://brainly.com/question/12198017
  3. Calculate the pH of an acidic buffer system https://brainly.com/question/9079717

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